Eur. Phys. J. D 30, 343–351 (2004) DOI: 10.1140/epjd/e2004-00103-6 T HE EUROPEAN P HYSICAL JOURNAL D From localised to delocalised electronic states in free Ar, Kr and Xe clusters R. Feifel 1 , 2, a , M. Tchaplyguine 1, 3 , G. ¨ Ohrwall 1 , M. Salonen 1, 4 , M. Lundwall 1 , R.R.T. Marinho 5 , M. Gisselbrecht 3 , S.L. Sorensen 6 , A. Naves de Brito 7, b , L. Karlsson 1 , N. M˚ artensson 1 , S. Svensson 1 , and O. Bj¨ orneholm 1 1 Department of Physics, Uppsala University, Box 530, 751 21 Uppsala, Sweden 2 Physical and Theoretical Chemistry Laboratory, Oxford University, South Parks Road, Oxford OX1 3QZ, United Kingdom 3 MAX-LAB, University of Lund, Box 118, 221 00 Lund, Sweden 4 Department of Physical Sciences, University of Helsinki, PO Box 33, 00014 Helsinki, Finland 5 Department of Physics, Bras´ ılia University, CEP 70910 900 Bras´ ılia DF, Brazil 6 Department of Synchrotron Radiation Research, Institute of Physics, University of Lund, Box 118, 221 00 Lund, Sweden 7 Lab´oratorio Nacional de Luz S´ ıncrotron (LNLS), Box 6192 CEP, 13084-971 Campinas, Brazil Received 5 March 2004 / Received in final form 4 May 2004 Published online 24 August 2004 – c  EDP Sciences, Societ`a Italiana di Fisica, Springer-Verlag 2004 Abstract. We present new results for the inner valence levels of clusters of the three inert gases Ar, Kr and Xe based on photoelectron spectroscopy studies. The inner valence levels are compared to the localised core levels and to the delocalised outer valence levels. This comparison shows a gradual change from a relatively localised behaviour for Ar inner valence 3s, over the intermediate case of Kr inner valence 4s, to a more delocalised behaviour for Xe inner valence 5s. This change correlates well with the ratio between the orbital sizes and the interatomic distances. The Kr4s intermediate case is found to exhibit characteristics of both localised and delocalised behaviour. PACS. 36.40.-c Atomic and molecular clusters – 36.40.Wa Charged clusters – 61.46.+w Nanoscale materials: clusters, nanoparticles, nanotubes, and nanocrystals 1 Introduction The electronic structure of atoms, molecules or larger polyatomic systems is usually divided into valence lev- els and core levels. Already for diatomic molecules it is well-known that in most cases the outer valence levels of the atoms overlap and become delocalised over the entire system. This is the basis of many physical and chemical properties. Core levels of neighbouring atoms, having sig- nificantly smaller spatial extent, are usually considered not to overlap. They are therefore considered to be lo- calised and are still atomic-like even in a large molecule or an infinite solid. The situation for the inner valence levels, i.e. the orbitals energetically located between the outer valence levels and the core levels, is much less clear and no general statement can be made. Clusters, as (artificial) aggregates of a finite number of building blocks, atoms or molecules, bridge the gap be- tween the isolated atom and the infinite solid (Ref. [1]). They give the possibility to study the development of ma- terial properties like chemical bonding, electrical conduc- tivity etc. as a function of a varying number of building a e-mail: raimund.feifel@fysik.uu.se b On leave from Dept. of Physics, University of Bras´ ılia, 70910-900 Bras´ ılia, Brazil. blocks (cluster size). The microscopic origin of physical and chemical properties is the electronic structure of a system. For clusters the above mentioned subdivision into outer valence, inner valence and core levels can in principle be made as well. The atomic-like character of core levels means in gen- eral that the binding energies of these levels are element specific. Beside the element specificity of core-levels, also small changes of the binding energy due to the local atomic environment, the so-called “chemical shifts”, can be en- countered. It is thus possible to distinguish different atoms of the same element located at different inequivalent sites in polyatomic systems. This is the basis of Electron Spec- troscopy for Chemical Analysis (ESCA) (see Ref. [2]). Rare gas clusters are important model systems to in- vestigate the development of certain properties and phe- nomena with size. They can be studied by a variety of experimental techniques. In particular, detailed knowl- edge about the electronic structure of free, neutral clus- ters is of fundamental interest and is rapidly expanding. Most of the studies performed so far have been made with X-ray absorption spectroscopy (see Refs. [3–5] and references therein) where essentially the unoccupied va- lence and Rydberg levels are probed. Several studies can be found in the literature on the occupied outer valence